Random Close Packing as a Dynamical Phase Transition

The densest packing of spheres, although known for millennia to be a Face-Centered Cubic (FCC) crystal with volume fraction φ~0.74, has only recently been proven mathematically by Hales. An equally ancient problem is “Random Close Packing”, RCP, the densest packing of spheres poured into a jar described in Biblical times (Luke 6:38, KJV) as, “pressed down, and shaken together, and running over”, a problem which has escaped a noncontroversial definition although many experiments and simulations agree to a value φ_RCP~0.64. Here we show that a simple model, “Biased Random Organization”, BRO, exhibits a dynamical phase transition between absorbing (non-overlapping) and active states that appears to have RCP as its critical endpoint. BRO, an absorbing state model, remains in the Manna (sand-pile) universality class. Such models are hyperuniform at critical, S(q→0)~q^α. For the Manna class, α_3D=0.25. At φ_cmax, we show that BRO and two other protocols for RCP have very similar S(q) with α~0.25. We conjecture that the highest density absorbing state for an isotropic RO or BRO model, produces an ensemble of configurations that characterizes the state conventionally known as RCP. This characterization requires neither randomness nor jamming which rather become emergent properties.